argue, contend, debate, fence - have an argument about something

brawl, wrangle - to quarrel noisily, angrily or disruptively; "The bar keeper threw them out, but they continued to wrangle on down the street"

spat - engage in a brief and petty quarrel

polemicise, polemicize, polemise, polemize - engage in a controversy; "The two historians polemicized for years"

fall out - have a breach in relations; "We fell out over a trivial question"